GLEN RIDGE PUBLIC SCHOOLS
Curriculum Guide
Course Title: CORE GEOMETRY
Subject: Mathematics
Grade Level: 11, 12
Department/School: Mathematics/Glen Ridge High School
Duration: Full Year
Number of Credits 5
Prerequisite: Core Algebra or Algebra I
Elective or Required: Elective
Author:
Date Submitted: Summer 2007
Course Description
Core Geometry
This course offers a comprehensive study of geometry. A variety of topics are explored at a level appropriate for the students enrolled in the course. Students explore these topics in a variety of ways through diversified lessons and activities. Algebraic concepts are revisited through the geometric problem solving. This course prepares students for Intermediate Algebra.
GLEN RIDGE PUBLIC SCHOOLS
MATHEMATICS MISSI ON STATEMENT
Mathematics
and Computer Science are an integral part of our lives. Students must be actively involved in their
mathematics education with problem solving being an essential part of the
curriculum. The mathematics and computer
science curricula should emphasize thinking skills through a balance of
computation, intuition, common sense, logic, analysis and technology. Students will be engaged and challenged in a
student-centered learning environment that is developmentally appropriate. Students will communicate mathematical ideas
effectively by applying hands-on manipulatives, basic computational skills,
mathematical models, and technology in order to solve practical problems.
The Mathematics Standards
consist of five statements, which describe what is essential to excellent
mathematics education, and presented a view of mathematics teaching and
learning that integrates the processes of mathematical activity, the content of
mathematics, and the learning environment in the classroom. The following standards were adopted by the
New Jersey State Board of Education.
This course will cover the
following Core Curriculum Content Standards:
STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS) ALL
STUDENTS WILL DEVELOP NUMBER SENSE AND WILL PERFORM STANDARD NUMERICAL OPERA- TIONS
AND ESTIMATIONS ON ALL TYPES OF NUMBERS IN A VARIETY OF WAYS.
Descriptive Statement: Numbers and
arithmetic operations are what most of the general public think about when they
think of mathematics; and, even though other area like geometry, algebra, and
data analysis have become increasingly important in recent years, numbers and
operations remain at the heart of mathematical teaching and learning. Facility with numbers, the ability to choose
the appropriate types of numbers and the appropriate operations for a given
situation, and the ability to perform those operations as well as to estimate
their results, are all skills that are essential for modern day life.
Number Sense
Numerical Operations
Estimation
STANDARD 4.2 (GEOMETRY AND MEASUREMENT) ALL STUDENTS
WILL DEVELOP SPATIAL SENSE AND THE ABILITY TO USE GEOMETRIC PROPERTIES,
RELATION- SHIPS, AND MEASUREMENT TO MODEL, DESCRIBE AND ANALYZE PHENOMENA.
Descriptive Statement: Spatial sense
is an intuitive feel for shape and space.
Geometry and measurement both involve describing the shapes we see all
around us in art, nature and the things we make. Spatial sense, geometric modeling, and
measurement can help us to describe and interpret our physical environment and
to solve problems.
Geometric Properties
Transforming Shapes
Coordinate Geometry
Units of Measurement
Measuring Geometric Objects
STANDARD 4.3 (PATTERNS AND ALGEBRA) ALL STUDENTS WILL
REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES AND SOLVE
PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES.
Descriptive Statement: Algebra is a
symbolic language used to express mathematical relationships. Students need to understand how quantities
are related to one another, and how algebra can be used to concisely express
and analyze those relationships. Modern
technology provides tools for supplementing the traditional focus on algebraic
procedures, such as solving equations, with a more visual perspective, with
graphs of equations displayed on a screen.
Students can then focus on understanding the relationship between the
equation and the graph, and on what the graph represents in a real-life
situation.
Patterns
Functions and Relationships
Modeling
Procedures
STANDARD 4.4 (DATA ANALYSIS, PROBABILITY, AND DISCRETE
MATHEMATICS) ALL STUDENTS WILL DEVELOP AN UNDERSTANDING OF THE CONCEPTS AND
TECHNIQUES OF DATA ANALYSIS, PROBABILITY, AND DISCRETE MATHEMATICS, AND WILL
USE THEM TO MODEL SITUATIONS, SOLVE PROBLEMS AND ANALYZE AND DRAW APPROPRIATE
INFERENCES FROM DATA.
Descriptive Statement: Data analysis,
probability, and discrete mathematics are important interrelated areas of
applied mathematics. Each provides
students with powerful mathematical perspectives on everyday phenomena and with
important examples of how mathematics is used in the modern world. Two important areas of discrete mathematics
are addressed in this standard: a third area, iterations and recursion, is
addressed in Standard 4.3 (Patterns and Algebra).
Data Analysis
Probability
Discrete Mathematics – Systematic Listing and Counting
Discrete Mathematics – Vertex-Edge Graphs and
Algorithms
STANDARD 4.5 (MATHEMATICAL PROCESSES) ALL STUDENTS
WILL USE MATHEMATICAL PROCESSES OF PROBLEM SOLVING, COMMUNICATION, CONNECTIONS,
REASONING, REPRESENTATIONS, AND TECHNOLOGY TO SOLVE PROBLEMS AND COMMUNICATE
MATHEMATICAL IDEAS.
Descriptive
Statement: The mathematical
processes described here highlight ways of acquiring and using the content knowledge and skills delineated in the first four
mathematical standards.
Problem Solving Reasoning
Communication Representations
Connections Technology
Curriculum
Description
UNIT I: TOOLS OF GEOMETRY
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Identify and predict patterns.
2. Define and identify basic geometric terminology.
3. Measure and construct segments and angles.
4. Identify and utilize the Coordinate Plane in problem solving.
5. Calculate and use appropriately the perimeter, circumference and area of geometric shapes.
Approximate duration: 14-15 days
UNIT II: REASONING
AND PROOF
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Identify the parts of conditional statements and their implications in geometry.
2. Apply deductive reasoning to proofs.
3. Use algebraic properties to prove algebraic concepts.
4. Prove angles congruent.
Approximate duration: 12-13 days
UNIT III: PARALLEL AND PERPENDICULAR LINES
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Identify parallel and perpendicular lines.
2. Prove lines are parallel, perpendicular or neither.
3. Apply The Polygon Angle- Sum Theorem.
4. Apply knowledge of slopes of lines to proving lines parallel, perpendicular or neither on the Coordinate Plane.
5. Construct parallel and perpendicular lines.
Approximate
duration: 16-17 days
UNIT IV: CONGRUENT TRIANGLES
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Identify and prove triangles congruent.
2. Use congruent triangles to show all parts are congruent.
3. Understand congruency principles associated with special triangles.
Approximate duration: 16-17 days
UNIT V: RELATIONSHIPS WITHIN TRIANGLES
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Construct and utilize properties associated with the midsegments and bisectors of triangles.
2. Reason indirectly.
3. Apply inequalities in triangles to problem solving situations.
Approximate duration: 12-13 days
UNIT VI: QUADRILATERALS
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Classify quadrilaterals.
2. Understand and utilize properties of parallelograms.
3. Utilize the Coordinate Plane in graphing parallelograms.
Approximate duration: 14-15 days
UNIT VII: SIMILARITY
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Identify similar polygons.
2. Prove triangles similar.
3. Use properties associated with similar figures to find the measures of sides and angles.
Approximate duration: 12-13 days
UNIT VIII: RIGHT TRIANGLES AND TRIGONOMETRY
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Use the Pythagorean Theorem and its converse in finding sides of right triangles.
2. Define and apply the tangent, sine and cosine functions to finding sides and angles of right triangles.
3. Solve problems involving the angles of elevation and angles of depression.
4. Define and use vectors in problem solving situations.
Approximate duration: 14-16 days
UNIT IX: TRANSFORMATIONS
CCCS: 4.1, 4.2, 4.3, 4.4, 4.5
Objectives:
Students will be able to:
1. Translate, reflect, rotate and dilate geometric shapes.
2. Define symmetry and classify geometric shapes based on their symmetry.
3. Repeat a transformation or series of transformations (composition) to tessellate a space.
Approximate duration: 14-16 days
UNIT X: AREA
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Find the areas of parallelograms, triangles and quadrilaterals.
2. Find the areas of regular polygons.
3. Apply properties of similar figures to find the areas and perimeters in other ways.
4. Find the areas of circles and sectors.
5. Find geometric probabilities.
Approximate duration: 15-17 days
UNIT XI: SURFACE AREA AND VOLUME
CCCS: 4.1, 4.2, 4.3, 4.4, 4.5
Objectives:
Students will be able to:
1. Find the surface areas of prisms, cylinders, cones and spheres.
2. Find the volumes of prisms, cylinders, cones and spheres.
3. Discover and apply principles of surface areas and volumes to similar solids.
Approximate duration: 12-14 days
UNIT XII: CIRCLES
CCCS: 4.1, 4.2, 4.3, 4.5
Objectives:
Students will be able to:
1. Identify a line tangent to a circle.
2. Identify chords, arcs and inscribed angles.
3. Find the angle measures and segment lengths associated with circles.
4. Graph
circles in the Coordinate Plane.
Approximate duration: 10-12 days
List of texts,
resources, and/or literature:
TEXTBOOK: Bass,
Charles, Hall, Johnson, Kennedy, Geometry,
Pearson Education, Inc., publishing as Pearson Prentice Hall,